On restricted systems of higher indeterminate equations
Eric Temple Bell · Transactions of the American Mathematical Society · 1921
By two examples we shall illustrate a means for deriving arithmetical properties of certain restricted forms.So little being known concerning the arithmetic of forms of higher degree, it is reasonable to develop what is offered by analysis.The method exemplified is of wide scope and easy applicability, and may possibly, in addition to giving new properties of integers, yield also, on starting from the appropriate associated forms of the second degree, information regarding current problems.It is a natural extension to forms of higher degree of the classic applications of elliptic functions to special quadratic forms.The method being new, we shall give the analysis for the first example in some detail.1. We take first a single restricted form (1) rey* + vx' -xry*